SOLUTION: Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 108 miles in the same time that Dana travels 99 miles. If Chuck's rate of travel is 3 mph more than Dana's, a

Question 115248: Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 108 miles in the same time that Dana travels 99 miles. If Chuck's rate of travel is 3 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Use the formula that Distance equals Speed times Time to solve this equation. In equation
form this is:
.

.
For Chuck, the distance he traveled was 108 miles. His speed was where the "c" indicates
it is Chuck's speed. Substituting these into the equation for chuck results in:
.

.
Solve this equation for T by dividing both sides by to get:
.

.
Meanwhile, Dana travels 99 miles in the same time. Let represent Dana's speed.
Substituting these values into the distance equation results in:
.

.
Solve this equation for T by dividing both sides by and it becomes:
.

.
So we have two equations for T ... one for Chuck and one for Dana. But, according
to the problem, both drivers drive for equal times. So the two T equations are equal. That
means the right sides of these equations are equal for the two drivers. So it can be said
that:
.

.
Next the problem tells you that Chuck's speed is 3 miles per hour more than Dana's. So
it also can be said that:
.

.
Substitute the right side of this into the Time equation and the result is:
.

.
Put both of these fractions over a common denominator by multiplying both sides of this
equation by . Note that since the numerator of this
multiplier is equal to the denominator, this is equivalent to multiplying both sides of the
equation by 1.
.
This multiplication leads to:
.

.
Cancel the like terms in the denominators and numerators on both sides:
.

.
This leaves:
.

.
Since the denominators are the same on both sides, the numerators must be equal. So, setting
the numerators equal results in:
.

.
Multiplying out the right side results in:
.

.
Subtract from both sides to get rid of that term on the right side and the
result is:
.

.
Solve for by dividing both sides by 9 to get:
.

.
So Dana's speed is 33 miles per hour. And Chuck's speed, which is 3 miles per hour faster,
is 36 miles per hour.
.
Check. At 36 miles per hour it will take Chuck 3 hours to go 108 miles. And at 33 miles per
hour, it will take Dana 3 hours to go 99 miles. The answer checks because the times are equal.
.
Hope this helps you to understand the problem and to see how it might be solved.
.

RELATED QUESTIONS
chuck and dana agree to meet in chicago for the weekend. Chuck travels 148 miles in the... (answered by mananth)

Translate the problem into a pair of linear equations in two variables. Solve the... (answered by mananth)

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 147 miles in the... (answered by mananth)

Solve the problem. Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels (answered by ankor@dixie-net.com)

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 84 miles in the... (answered by gonzo)

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 160 miles in the... (answered by checkley77)

Chuck and Dana agree to meet in chicago for the weekend. Chuck travels 174 miles in the... (answered by ewatrrr)

chuck and dana agree to meet in chicago for the weekend. Chuck travels 276 miles in the... (answered by josmiceli)

translate the problem into a pair of linear equations in two variables. solve the... (answered by stanbon)